It is well known to provide printing machine cylinders with axial grooves on which essentially circular plates or rubber blankets, respectively, can be clamped. Printing machines,and especially sheet-fed offset printing machines, frequently use an intermediate underlay made of paper or cardboard in order to accurately adjust the diameter and the tensioning of the cover about a cylinder. German Pat. No. 1,145,185 describes an arrangement in which an underlay is retained in the cylinder groove in the space between the wall of the cylinder groove and a tensioning rod. The tensioning rod is eccentrically journalled or eccentrically constructed, and upon rotation of the eccentric tensioning rod, the underlay is clamped or pressed against the wall of the groove. The construction is comparatively complex and, particularly when used with large-format printing machines, requires careful adjustment and handling so that the engagement pressure throughout the axial length with be essentially uniform.